Halting Brexit and bringing about a "real end to austerity" were also among the "progressive policies" Ms Sturgeon would push for if there is a hung Parliament after the December 12 General Election.
She insisted these would "resonate strongly with many people across the UK", as well as her supporters in Scoltand.
The SNP leader made the comments as Labour's shadow chancellor John McDonnell said it could be "two or three years" before a Jeremy Corbyn administration would give the go-ahead for Scotland to have a second vote on leaving the United Kingdom.
Ms Sturgeon - who has already said she wants a fresh ballot on independence to take place in the second half of 2020 - said that stance was not acceptable.
Speaking on the Sophy Ridge on Sunday programme on Sky News, she said: "My position, and the one I would expect Labour to respect if they wanted SNP support, is the question of if there is an independence referendum and the time of that is down to the Scottish Parliament to decide, not Westminster."
The SNP leader questioned if Labour "against what all the opinion polls might be suggesting" were able to form a minority government after December 12 "are they really going to turn their back on the chance to stop austerity, to stop welfare cuts, to get rid of Universal Credit, because they want to block the right of people to decide their own future and argue over a couple of years?".
She insisted an election which ended up with a hung Parliament where the SNP held the balance of power"would give Scotland maximum influence".
She added: "That would be a pretty good outcome I think in terms of making sure Scotland's voice is heard."
She repeated her assertion that the SNP would "never, ever put Boris Johnson into Downing Street" and that she would not enter into a formal coalition with Mr Corbyn, saying instead there would be a "less formal arrangement".
Ms Sturgeon also said the SNP would have other key demands, including halting Brexit, a "real end to austerity", the devolution of powers over migration, workers' rights, and drugs laws, and "an end to the misery of Universal Credit and welfare cuts".
Her comments came after Mr McDonnell told the same programme a Labour government would not support a second independence vote in "those first few years when we're getting on with the job".
Labour has been repeatedly forced to clarify its stance on permitting a second independence referendum, with Mr Corbyn initially saying such a ballot could not take place in the first five-year parliamentary term if he was prime minister, before saying this would not take place in the "early years" and "certainly not" in the first two years.
Mr McDonnell stated: "I wouldn't expect anything in the first two or three years because the Scottish people themselves are saying we've got to concentrate on austerity and get that sorted.
"We've got to concentrate on sorting out Brexit. Above all else we've got an existential threat of climate change. That's a huge agenda.
"We see the independence issue in terms of a potential referendum as a distraction from that."
He insisted there would be no change to that stance, even if the SNP made holding a referendum in 2020 a red line in post-election negotiations.